Digital servo systems using the state feedback method have been widely used in the fields such as hard disk drive (HDD), robotics and aircraft to improve control performance. FIG. 1 shows a schematic configuration of such a system. As seen, state variables representing the internal state of a plant 10 (for example, an actuator of HDD) are fed back, through a multiplier 12, to the input side of the plant 10. Input to the plant 10 is obtained by adding outputs of the multipliers 12 and 14. Input to the multiplier 14 is provided by an internal model 16 which receives a signal indicating a difference between the output of the plant 10 and a target value.
It is well known in the art that in designing such a servo system as shown in FIG. 1, it is important to make the output of a plant follow a target value without any steady state deviation, and to this end it is necessary to insert a model for generating a target value (called an internal model) in a closed loop of a control system. The internal model 16 is inserted for this purpose. For example, if a target value is constant (step input), an integrator may be used as the internal model because such a target value can be generated by providing an appropriate initial value to the integrator. In the servo system of FIG. 1, feedback gains to be obtained in the servo system design are coefficients -F1 and -F2 which are multiplied in the multipliers 12 and 14, respectively.
If the state variables of the plant 10 cannot be directly observed, a state estimator (also called observer) 18 is used for estimating the state variables based on the input and output of the plant, as shown in FIG. 2. A general discussion about a state estimator is found, for example, in Iwai et al, Observer, Corona (1988). Also, U.S. Pat. No. 4,679,103 assigned to the present assignee discloses a digital servo control system for controlling a data recording disk file using such a state estimator in which the state estimator receives a position error signal (PES) obtained by demodulating servo information read from a disk and input to an actuator which is a plant, and outputs estimated values of position, velocity, and acceleration of a head which are state variables.
Now the systems of FIG. 1 and FIG. 2 are described in more detail. Assuming that a plant is a controllable and observable linear system, and its input, output and state variables at a sampling time i(.gtoreq.0) are u(i), y(i) and x(i), respectively, then a mathematical model of its discrete time system is generally represented by the following equations.